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File:TorusSystoleLoop.png

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Original file (1,078 × 887 pixels, file size: 132 KB, MIME type: image/png)

Summary

Description
English: A torus with varying tube radius with another torus indicating the smallest radius of the tube.
Date
Source Own work using MATLAB
Author RobHar
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


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Data file

This graphic was created in MATLAB using the following code:

%create u-v grid space
u=linspace(0,2*pi,120);
v=linspace(0,2*pi,120);
[u,v]=meshgrid(u,v);

R=0.5;                      %set large radius of torus
r=abs(cos(v/2))*0.2+0.05;   %set small radius to vary with angle

%parametrization
x=(R+r.*cos(u)).*cos(v);
y=(R+r.*cos(u)).*sin(v);
z=r.*sin(u);

H=surf(x,y,z);
hold on;			    %put a hold on this figure
set(H,'FaceColor',[0.25 0.25 0.75],'EdgeColor','none');
set(H,'SpecularColorReflectance', 0.2, 'DiffuseStrength', 0.8);
set(H,'AmbientStrength', 0.3,'FaceLighting','phong');
set(H,'SpecularExponent', 100);

daspect([1 1 1]);   %set ratio of x,y,z axes
axis tight;         %fit axes to figure
axis off;           %don't show axes
view(190, 40);      %set viewing angle
camlight (-50, 54); lighting phong; %add light source

%add another torus to show tightest place on the torus
R2=0.075;
r2=0.025;

x2=(R2+r2.*cos(u)).*cos(v)-0.5;
y2=r2.*sin(u);
z2=(R2+r2.*cos(u)).*sin(v);

H2=surf(x2,y2,z2);
set(H2,'FaceColor',[0.75 0.25 0.25],'EdgeColor','none');
set(H2,'SpecularColorReflectance', 0.2, 'DiffuseStrength', 0.8);
set(H2,'AmbientStrength', 0.5,'FaceLighting','phong');
set(H2,'SpecularExponent', 100);

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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depicts

19 December 2008

File history

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Date/TimeThumbnailDimensionsUserComment
current18:35, 19 December 2008Thumbnail for version as of 18:35, 19 December 20081,078 × 887 (132 KB)RobHar{{Information |Description={{en|1=A torus with varying tube radius with another torus indicating the smallest radius of the tube.}} |Source=Own work using MATLAB |Author=RobHar |Date=2008-12-19 |Permission= |other_versions= }} <!--{{Image

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